Elliptic flow in the Gaussian model of eccentricity fluctuations

We discuss a specific model of elliptic flow fluctuations due to Gaussian fluctuations in the initial spatial x and y eccentricity components {〈(σy2−σx2)/(σx2+σy2)〉,〈2σxy/(σx2+σy2)〉}. We find that in this model v2{4}, elliptic flow determined from 4-particle cumulants, exactly equals the average flow value in the reaction plane coordinate system, 〈vRP〉, the relation which, in an approximate form, was found earlier by Bhalerao and Ollitrault in a more general analysis, but under the same assumption that v2 is proportional to the initial system eccentricity. We further show that in the Gaussian model all higher order cumulants are equal to v2{4}. Analysis of the distribution in the magnitude of the flow vector, the Q-distribution, reveals that it is totally defined by two parameters, v2{2}, the flow from 2-particle cumulants, and v2{4}, thus providing equivalent information compared to the method of cumulants. The flow obtained from the Q-distribution is again v2{4}=〈vRP〉.